`[-(1)/(3)]+[-(1)/(3)-(1)/(100)]+[-(1)/(3)-(2)/(100)]+….+[-(1)/(3)-(99)/(100)]` is equal to (where `[.]` denotes greatest integer function)

Explanation

To solve the expression

\[ [-(1)/(3)] + [-\frac{1}{3} - \frac{1}{100}] + [-\frac{1}{3} - \frac{2}{100}] + \ldots + [-\frac{1}{3} - \frac{99}{100}] \]

we will analyze each term step by step.

### Step 1: Identify the general term
The general term of the sequence can be expressed as:

\[ T_n = -\frac{1}{3} - \frac{n}{100} \]

where \( n \) ranges from 0 to 99.

### Step 2: Calculate the first term
For \( n = 0 \):

\[ T_0 = -\frac{1}{3} - \frac{0}{100} = -\frac{1}{3} \]

### Step 3: Calculate the second term
For \( n = 1 \):

\[ T_1 = -\frac{1}{3} - \frac{1}{100} = -\frac{100}{300} - \frac{3}{300} = -\frac{103}{300} \]

### Step 4: Calculate the third term
For \( n = 2 \):

\[ T_2 = -\frac{1}{3} - \frac{2}{100} = -\frac{100}{300} - \frac{6}{300} = -\frac{106}{300} \]

### Step 5: Generalize the term
Continuing this pattern, we can see that:

\[ T_n = -\frac{100 + 3n}{300} \]

### Step 6: Determine when the greatest integer function changes
We need to find when \( T_n \) crosses the integer boundaries. The greatest integer function \( [x] \) will yield different values depending on the value of \( T_n \).

1. For \( n = 0 \) to \( n = 66 \):

\[ T_{66} = -\frac{100 + 3 \cdot 66}{300} = -\frac{298}{300} \]

This is between -1 and 0, so:

\[ [T_n] = -1 \quad \text{for } n = 0 \text{ to } 66 \]

2. For \( n = 67 \):

\[ T_{67} = -\frac{100 + 3 \cdot 67}{300} = -\frac{301}{300} \]

This is less than -1, so:

\[ [T_{67}] = -2 \]

### Step 7: Count the contributions
- From \( n = 0 \) to \( n = 66 \) (67 terms), each contributes -1:

\[ 67 \times (-1) = -67 \]

- From \( n = 67 \) to \( n = 99 \) (33 terms), each contributes -2:

\[ 33 \times (-2) = -66 \]

### Step 8: Sum the contributions
Now, we can sum the contributions:

\[ -67 + (-66) = -133 \]

### Final Answer
Thus, the value of the given expression is:

\[ \boxed{-133} \]